Can you leave a tour group?

Tour groups are great for many things. They preplan trips so you don't need to do bookings, and they get incredibly cheap prices. Yet, I hate following their itinerary. I've never been to a country with a tour group, but is it possible for me just to use them to get to my country, then do things on my own? Like, I'll meet up with them when I want to do what they are doing or when its time to leave for another city, but the rest of the time (meals, sightseeing, ect) can I just leave?